Question

a half cylinder with a diameter of 2 mm is 9n top of a rectangular prism. A second half cylinder with a diameter of 4 mm is on the side of the prism. All shapes are 5 mm long. What is the volume of the combined figures?

Answer 1

The volume will be given by:

The volume of the half cylinder on top, plus the volume of the rectangular prims, plus the volume of the half cylinder on the right:

so:

The volume of the half cylinder on top is:

`\begin{gathered} V1=(\pi r^2l)/(2) \\ V1=(\pi(1^2)5)/(2)=(5\pi)/(2) \end{gathered}`

The volume of the half cylinder on the right is:

`\begin{gathered} V2=(\pi r^2l)/(2) \\ V2=(\pi(2^2)\cdot5)/(2)=10\pi \end{gathered}`

The volume of the rectangular prism is:

`\begin{gathered} V3=l\cdot w\cdot h \\ V3=4\cdot2\cdot5 \\ V3=40 \end{gathered}`

Therefore, the total volume is:

`\begin{gathered} Vt=V1+V2+V3 \\ Vt=(5)/(2)\pi+10\pi+40=79.3mm^3 \end{gathered}`